Have you picked a weapon yet? Different guns have different capacities.

Yup! You can get a Glock and then buy a 30rd mag for it. Or you can get that XDM9 thing and those mags hold 19. Those are just handguns brother!
Next is rifles and shotguns and such! Keep cruising this place and you'll know exactly the questions to ask to get the responses you need. Surprisingly this place has allot of smart people apposed to other forums with there trolls etc.

Well, I'm thinking of having this character (a 22 year old woman) use a 9mm handgun, and I'm hoping there's one with maybe around 20 round capacity, because she's something of a klutz with her hands and has difficulty reloading weapons quickly.

Also, I've heard of automatic weapons that can have the automatic firing "turned off." If this is true, I'm thinking that another character who gets his hands on some machine guns would do this with a large magazine assault rifle after discovering that the AK 47 only has three seconds of continuous fire, despite what every single action movie ever would suggest.

As was said earlier 9mm is not heavy. It would be easy to carry several hundred rounds in a pack and still have load capacity for other gear like clothing, cookware, and eats. It would be a fairly scarce load,though to keep it within a reasonable weight. I have a get home bag that has about 6 pounds of ammo in it. If it were a bug out bag I would make that number a lot higher and get rid of something to make up for the weight.

I pulled a plastic ammo box from my pack and weighed it as 1.425 pounds with 9mm Winchester 115 gr. JHP ammo.

As far as round capacity I do not believe outside of a couple of states with obnoxious gun restrictions, there is a limit to round capacity. You can easily get 100 round drum magazines for AR15's and AK's. Pistol mag capacity varies with model.

I will stick with 9mm as you suggested. Not common for a revolver which would hold 5 or 6. Pocket pistols generally have a smaller magazine and will hold 8-10. Full size pistols will go from 10 to 30, with the middle of that being most common. Newer models generally have higher capacity, manufacturers have seen the demand and are building to it.

10 to 30 round capacity 9mm handguns? I must not be looking in the right place, then. I looked up 9mm handguns, found a website that sold them, and the largest magazine size I found held 19 bullets. What handgun uses 30 9mm round magazines?

Of course writing about what you know would be good. There was an author I read recently whose main character (an FBI agent) always loaded his .45acp Glock 30 by 1) putting in a full magazine, 2) pulling back the slide and 3) hand-placing a single round into the chamber. The author described it this way several times. There are a few problems with that procedure, but the author didn't have enough personal knowledge to know how laughable it was.

Most magazines for hand guns do not have such an even number as 20 or 30. Even the high-capacity magazines for 9mm Glocks (SecPro doesn't know what he's talking about on this one) hold 33 rounds, not 30. 15 rounds and 17 rounds is pretty common.

Also, if someone was carrying around a lot of ammo, much of it would be pre-loaded into magazines, one could presume, for quick use.

10 to 30 round capacity 9mm handguns? I must not be looking in the right place, then. I looked up 9mm handguns, found a website that sold them, and the largest magazine size I found held 19 bullets. What handgun uses 30 9mm round magazines?

The Glock series of 9mm handguns (models 17, 18, 19, 26...) have the option of buying a 33-round magazine, which sticks out the bottom. Go to Youtube and look for Glock 18. You can also search for Glock magazines and you will find other sizes of mags. The 33-round magazine would only be used for a few reasons, though, since it is so unwieldy (range shooting for fun and killing people are two reasons I can think of).

The Glock 18, by the way, is not available in the US because it has a little switch that makes it go from semi-automatic (1 round per pull of the trigger) to fully automatic. A 33-round magazine goes very quickly.

Guns that fire 3-round bursts are NOT handguns. Someone here will correct me if I'm wrong, though. That concept is from the military's M-16, which is a rifle and can be selected to fire 1-round, 3-round bursts, or fully automatic.

Most magazines for hand guns do not have such an even number as 20 or 30. Even the high-capacity magazines for 9mm Glocks (SecPro doesn't know what he's talking about on this one) hold 33 rounds, not 30. 15 rounds and 17 rounds is pretty common.

Yeah I messed this one up but I chalk it up to not owning a Glock...
These mags aren't common like CHLChris said, but they are available.